Heat 1 tbsp oil over medium-high heat in a large cast-iron skillet or a wok. When oil is shimmering hot, add pork and cook, breaking up with a spoon, until cooked through and starting to crisp up.
Meanwhile, whisk 3/4 cup chicken stock with peanut butter, soy sauce, brown sugar, garlic and chiles in a large mixing bowl (you need a lot of room to whisk in the peanut butter). Set aside.
Using a slotted spoon, transfer cooked pork to a bowl. Pour fat from pan and discard. Add remaining 1/4 cup chicken broth to pan and return to medium heat. Deglaze the pan by scraping the bottom to release all browned bits. Pour into bowl with pork.
Add 4 tbsp oil to same pan over medium-high heat. Add onion, cabbage, carrots and gai lan stalks. Cook, stirring frequently, until cabbage is tender, about 4 minutes. Stir in gai lan leaves and cook until just wilted. Return pork to pan, add sauce and cook, tossing with tongs, until well combined and heated through. Serve topped with peanuts with lots of lime wedges on the side.